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In this article we introduce a gluing orbit property, weaker thanspecification, for both maps and flows. We prove that flows with the$C^1$-robust gluing orbit property are uniformly hyperbolic and that everyuniformly hyperbolic flow satisfies the gluing orbit property. We also prove alevel-1 large deviations principle and a level-2 large deviations lower boundfor for semiflows with the gluing orbit property. As a consequence we establisha level-1 large deviations principle for hyperbolic flows and every continuousobservable, and also a level-2 large deviations lower bound. Finally, sincemany non-uniformly hyperbolic flows can be modeled as suspension flows we alsoprovide criteria for such flows to satisfy uniform and non-uniform versions ofthe gluing orbit property.

The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows